Solve 243x^4y-3y^5

$$243 x ^ { 4 } y - 3 y ^ { 5 }$$

Factor

$$3y\left(3x-y\right)\left(3x+y\right)\left(9x^{2}+y^{2}\right)$$

Solution Steps

Factor out 3.

$$3\left(81x^{4}y-y^{5}\right)$$

Consider 81x^{4}y-y^{5}. Factor out y.

$$y\left(81x^{4}-y^{4}\right)$$

Consider 81x^{4}-y^{4}. Rewrite 81x^{4}-y^{4} as \left(9x^{2}\right)^{2}-\left(y^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9x^{2}-y^{2}\right)\left(9x^{2}+y^{2}\right)$$

Consider 9x^{2}-y^{2}. Rewrite 9x^{2}-y^{2} as \left(3x\right)^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-y\right)\left(3x+y\right)$$

Rewrite the complete factored expression.

$$3y\left(3x-y\right)\left(3x+y\right)\left(9x^{2}+y^{2}\right)$$

Evaluate

$$243yx^{4}-3y^{5}$$